The purpose of this activity is to provide a diagnosis and remediation strategy for students who have difficulty understanding what it means to multiply fractions.
When using virtual manipulatives, third grade students can accurately interpret, display, and answer what is 1/4 of 4. However, they cannot interpret and answer what is 1/4 of 8. The student does not know where to start.
Step One: Ask the student to go back to the 4 block example and ask "Why is the answer 1 block?" Look for student to describe that 1 is 1/4th of 4. The student should be able to describe what the numerator and denominator of 1/4 represent. The denominator describes the number of equal parts in the whole group (4), and that the 1/4 represents 1 out of the 4 blocks.
Step Two: Ask the student "what is 1/3 of 3?", then ask "what is 1/3 of 6?" This will help determine whether it is an isolated event with 4 blocks.
Diagnosis: The student may not understand what a whole (denominator) represents.
Remediation: What we want students to understand is that 2 of 8 pieces in a whole is the same amount as 1 of 4 equal parts of that whole.
The Fraction Pieces applet from the National Library of Virtual Manipulatives may help in visualizing this objective.
Another possible remediation activity is to have students get into a group of 8. Split the group of 8 into 2 groups of 4, and have a student say "1/2 of 8 is 4 students." Ask students to illustrate 1/2 group of 8 students, 4 students. Have the students model step 1 using manipulatives. Have the students model step 1 using the symbols 1/2 of 8 is (equal to) 4 and 1/2 x 8 = 4. The purpose of this suggestion is to make sure students are able to link symbols with appropriate terms.
Assessment: Students who understand what it means to take a fractional amount of a set of things will be able to accurately describe the question, and illustrate the result.
Understanding Multiplication of Fractions
The purpose of this activity is to provide a diagnosis and remediation strategy for students who have difficulty understanding what it means to multiply fractions.
When using virtual manipulatives, third grade students can accurately interpret, display, and answer what is 1/4 of 4. However, they cannot interpret and answer what is 1/4 of 8. The student does not know where to start.
Step One: Ask the student to go back to the 4 block example and ask "Why is the answer 1 block?" Look for student to describe that 1 is 1/4th of 4. The student should be able to describe what the numerator and denominator of 1/4 represent. The denominator describes the number of equal parts in the whole group (4), and that the 1/4 represents 1 out of the 4 blocks.
Step Two: Ask the student "what is 1/3 of 3?", then ask "what is 1/3 of 6?" This will help determine whether it is an isolated event with 4 blocks.
Diagnosis: The student may not understand what a whole (denominator) represents.
Remediation: What we want students to understand is that 2 of 8 pieces in a whole is the same amount as 1 of 4 equal parts of that whole.
The Fraction Pieces applet from the National Library of Virtual Manipulatives may help in visualizing this objective.
Another possible remediation activity is to have students get into a group of 8. Split the group of 8 into 2 groups of 4, and have a student say "1/2 of 8 is 4 students." Ask students to illustrate 1/2 group of 8 students, 4 students. Have the students model step 1 using manipulatives. Have the students model step 1 using the symbols 1/2 of 8 is (equal to) 4 and 1/2 x 8 = 4. The purpose of this suggestion is to make sure students are able to link symbols with appropriate terms.
Assessment: Students who understand what it means to take a fractional amount of a set of things will be able to accurately describe the question, and illustrate the result.